Mixed boundary value problem for p-harmonic functions in an infinite cylinder

We study a mixed boundary value problem for the p-Laplace equation Δpu=0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. Existence of weak solutions to the mixed problem is proved both for Sobole...

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Vydáno v:Nonlinear analysis Ročník 202; s. 112134
Hlavní autoři: Björn, Jana, Mwasa, Abubakar
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Ltd 01.01.2021
Témata:
[formula omitted]-Laplace equation
Boundary regularity
Capacity
Dirichlet and Neumann data
Existence of weak solutions
Mixed boundary value problem
Unbounded cylinder
Wiener criterion
secondary
Existence of weak solutions
Mixed boundary value problem
Capacity
p-Laplace equation
Wiener criterion
Boundary regularity
Unbounded cylinder
primary
Dirichlet and Neumann data
ISSN:0362-546X, 1873-5215, 1873-5215
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Shrnutí:We study a mixed boundary value problem for the p-Laplace equation Δpu=0 in an open infinite circular half-cylinder with prescribed Dirichlet boundary data on a part of the boundary and zero Neumann boundary data on the rest. Existence of weak solutions to the mixed problem is proved both for Sobolev and for continuous data on the Dirichlet part of the boundary. We also obtain a boundary regularity result for the point at infinity in terms of a variational capacity adapted to the cylinder.
ISSN:0362-546X
1873-5215
1873-5215
DOI:10.1016/j.na.2020.112134